# Is the answer also imaginary?

Algebra Level 4

If $$\omega$$ is one of the imaginary cube roots of unity,evaluate$\left | \begin{array}{cccc} 1 & \omega & \omega^2 & \omega^3 \\ \omega & \omega^2 & \omega^3 & 1 \\ \omega^2 & \omega^3 & 1 & \omega \\ \omega^3 & 1 & \omega & \omega^2 \end{array} \right |^{2}.$ If the value of above determinant is in the form $$a+b\sqrt{-1}$$, find $$a+b$$.

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